Dennis Lindley - obituary

Dennis Lindley was the 'High Priest of Bayesianism’ who saw in statistics a
way of dealing with the uncertainties of everyday life

Dennis Lindley

6:54PM BST 10 Apr 2014

Dennis Lindley, who has died aged 90, was a statistician who became a leading advocate of a controversial but increasingly popular approach known as Bayesianism.

The Bayesian school takes its name from Thomas Bayes, an 18th-century Presbyterian minister and mathematician who, in a paper entitled An Essay towards solving a Problem in the Doctrine of Chances, outlined a method to evaluate probability which allowed for adjustments in the light of new evidence.

Bayesian statistical methods start with existing “prior” beliefs, and update these gradually using data to give “posterior” beliefs, according to a standard set of procedures and formulae – in order to provide a basis for inferring probability and making decisions.

Bayesian statistical methods are increasingly (though by no means universally) used, for example, where a policy decision must be made on the basis of a combination of imperfect evidence, or where a problem must be solved on the basis of multiple sources of evidence. Using such data, the Bayesian statistician formulates “probability distributions” to express the uncertainty involved. Bayesian methods have caught on particularly in such fields as market research, in some branches of econometrics and in computer learning and filtering systems, such as those which distinguish between “spam” and “non-spam” emails.

Lindley envisioned the approach as a way of understanding and handling uncertainty in our everyday lives. “There are some things that you know to be true, and others that you know to be false,” he wrote; “yet, despite this extensive knowledge that you have, there remain many things whose truth or falsity is not known to you. We say that you are uncertain about them. You are uncertain, to varying degrees, about everything in the future; much of the past is hidden from you; and there is a lot of the present about which you do not have full information. Uncertainty is everywhere and you cannot escape from it... it is not the uncertainty, but your uncertainty.”

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Though Lindley rejected religious metaphors, Bayesianism has often been seen, by its critics, as a quasi-religious movement of which Lindley was sometimes described as the “high priest” in Britain.

In 1967 when he was appointed to the leading chair of statistics at University College London (a one-time bastion of statistical orthodoxy) a colleague commented : “Good Heavens! It’s as though a Jehovah’s Witness has been elected Pope.”

The only child of a builder, Dennis Victor Lindley was born in south London on July 25 1923 and brought up in Surbiton. In an interview in 1994 he recalled that his parents had “little culture” and were “proud of the fact that they had never read a book and they had a low opinion of classical music”. It was only when he went to Tiffin School, Kingston-upon-Thames, that he realised that there “were other things in the world”.

At first Dennis wanted to be an architect and his father made plans for him to leave school and become an apprentice. But war intervened and made it difficult, so he was allowed to stay on and sit for higher level exams. He did so well in mathematics that his teacher managed to persuade his parents that he should try for Cambridge.

During the Blitz Tiffin pupils often had to take refuge in the school shelters. There, since the mathematics teacher could not teach the whole class, he used the time to give his prize pupil individual tuition. Lindley won an exhibition to Trinity College (for which he later gave due credit to Hitler).

He went up to Cambridge in 1941, when the degree course was shortened to two years due to the war. After graduation he joined the Ministry of Supply as a statistician, working on introducing statistical quality control and inspection into arms production.

After the war Lindley spent some time at the National Physical Laboratory before returning to Cambridge for a further year of postgraduate study. From 1948 to 1960 he worked at Cambridge, rising to the position of director of the Statistical Laboratory.

Lindley always worked from first principles – or axioms – and as an undergraduate had been frustrated that the only branch of mathematics in which axiomatic reasoning had been seen as irrelevant was statistics. Students were trained in “frequentist” statistical techniques and methodology, but were not encouraged to examine or test the underlying principles.

On his appointment to an assistant lectureship Lindley decided to try to establish a rigorous axiomatic justification for “frequentism”. It was in the course of this work he began to detect flaws in the classical approach and moved to a Bayesian stance.

In 1960 Lindley was appointed Professor of Statistics at Aberystwyth and seven years later he moved to University College London.

Lindley took early retirement in 1977 and devoted the next 10 years to travelling the world as an “itinerant scholar”.

He published more than 100 significant scholarly articles and several books, including Introduction to Probability and Statistics from a Bayesian Viewpoint (2 volumes, 1965) and Understanding Uncertainty (2006). In 1979 he founded the Valencia International Meetings on Bayesian Statistics, held every four years, and in 2002 was awarded the Royal Statistical Society’s Guy Medal in Gold.

In 1947 he married Joan Armitage, with whom he had a daughter and two sons.